Figure REF  shows the histogram for the unknown data distribution, as well as three curves calculated from [1]}'s algorithm's random walk. We simulate 150k draws from [1]}'s algorithm with half as burn-in. The top curve was calculated by taking the 95th percentile of curve values at each knot, then linearly interpolating between these points. The bottom curve was calculated in the same way, except using the 5th percentile. Note that neither of these curves need be feasible. The curve that minimizes the squared distance (on the ambient space) from all other curves is used as a point estimate. For the set \(\Theta ^*\)  of parameter vectors simulated by this MCMC method, the point estimate \(\hat{\theta }\)  is equal to
\( \hat{\theta } = \min _{\theta \in \Theta ^*} || \theta - \bar{\theta } ||_2, \) 
